What do Noisy Datapoints Tell Us About the True Signal?

Every measurement has uncertainty which needs to be quantified.
Bayesian approaches achieve this naturally, by expressing results in
terms of probabilities. I will give a conceptual overview of Bayesian
analysis for metrological applications. This includes a discussion of
Occam's razor, a helpful but qualitative dictum that is clarified and
quantified when recast in the language of probability. Three example
systems will illustrate these concepts: finding the true X-ray
diffraction curve from noisy count data, interpolating the strain
field of a stretched metal plate, and measuring aggregate uncertainty
in flame speed datasets. All these systems require us to calculate
probabilities for arbitrary smooth functions without assuming a
functional form, and I will explain how to do this in a Bayesian
context. Having quantified the uncertainty, I will also show several
ways to represent it, including smooth animations of sequences of
candidates for the true signal.

Speaker Bio:
Dr. Charles R. ("Chip") Hogg obtained a M.S. and Ph.D. in Physics from
Carnegie Mellon University in Pittsburgh, after earning a B.Sc. from
Brock University in Canada with a double major in Computer Science and
Physics. Since October 2010 he has been a Guest Researcher in the
Ceramics Division at NIST, supported by a NIST-ARRA postdoctoral
fellowship. He is broadly interested in applying Bayesian methods to
the physical sciences; his recent work has heavily involved
nonstationary Gaussian Processes with applications to local atomic
structure determination.